On the existence and the structure of the pseudo-equilibrium manifold

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1) ; a robust example of such economies is provided . Theorem 2 establishes that the manifold fl of global pseudo-equilibria is a fiber bundle with the topological structure of a oneor two-fold covering space of G k . ", the space of k planes in R", where k is the number of assets in the economy and n the number of states of uncertainty . In particular, the pseudo-equilibrium manifold dZ is not contractible with incomplete markets . This contrasts with the case of complete markets, where the equilibrium manifold is always contractible .